This work presents a hybrid analytical/numerical approach for transient heat conduction through composite hollow cylinder structures applied for Plug and Abandonment (P&A). The Distribution Transfer Function Method (DTFM) is a mathematical framework able to solve both nonhomogeneous boundary conditions and a nonlinear partial differential equation with spatial-temporal source term, presenting good agreement with Finite Element Method (FEM) and other analytical approaches. A new technology of Thermal Plug and Abandonment (TP&A) devoted for P&A operation is studied in this work, where a heat generator is used to melt the first layer of the well structure. The heat source will be modeled using thermite within the oil well manifold structure, which must be descended to desirable depths along the borehole through a cylindrical container. After an exothermic reaction the temperature fields will be determined by means of DTFM method. A novel adaptative step-wise procedure applied for DTFM allows one to solve non-differentiable heat flux, thermal and volumetric heat source profiles which exact quadrature regression are not able to solve. This method provides simple replicability, which can be reproduced for many emerging fields where transient heat conduction is an important parameter to be accounted for. Using experimental data as input in DTFM provides insight that the temperature response overcame the design melting point of the production tube, being capable of melting down the production tubing wall, which is a valuable achievement for oil industries since not removing the production tubing can save a great amount of time, and hence save costs for oil industries.

这项工作提出了一种混合分析/数值方法，用于通过用于即插即用（P＆A）的复合空心圆柱结构进行瞬态热传导。分布传递函数法（DTFM）是一个数学框架，能够解决非均匀边界条件和具有时空源项的非线性偏微分方程，与有限元方法（FEM）和其他分析方法具有很好的一致性。在这项工作中，研究了一种专门用于P＆A操作的热插拔放弃（TP＆A）新技术，其中使用了一个热发生器来熔化井结构的第一层。热源将在油井歧管结构内使用铝热剂进行建模，必须通过圆柱形容器沿钻孔将其降到所需深度。放热反应后，将通过DTFM方法确定温度场。一种适用于DTFM的新颖的自适应分步程序允许解决不可微的热通量，热和体积热源分布图，而精确的正交回归无法解决这些问题。该方法提供了简单的可复制性，可以在瞬态热传导是要考虑的重要参数的许多新兴领域中进行复制。使用实验数据作为DTFM的输入，可以发现温度响应超过了生产管的设计熔点，能够熔化生产管壁，这对于石油工业来说是一项宝贵的成就，因为不拆除生产管可以节省成本。大量的时间，从而节省了石油行业的成本。